Antenna Gain & EIRP

9006-003

9006-003a

The gain of a 100% efficient antenna over an isotropic radiating or receiving antenna is given by:

    4.pi.A
G = ------
      Wl2

where:

A = A_t for area of transmitting antenna or telescope (78.5 m²),
A = A_r for area receiving antenna or telescope (78.5 m²),
Wl = wavelength (656 nm).

The gain is normally expressed in dBs by taking 10.log(G).

For the above 10 meter diameter telescope:

G = 2.29 x 10¹⁵ = 153.6 dB

9006-003b

The Effective Isotropic Radiated Power (EIRP) is the apparent power transmitted towards the receiver, if it is assumed that the signal is radiated equally in all directions, i.e. as a spherical wave emanating from a point source. This power is given by:

EIRP = Gt.Pt  Watts

where:

G_t = gain of transmitter antenna or telescope (153.6 dB),
P_t = power transmitted (1 kW).

For the above 1 kW visible transmitter:

EIRP = 2.29 x 10¹⁸ W

This is a little over one million trillion watts! Now the Sun has a radius of 6.96 x 10⁸ m and a luminosity of 3.9 x 10²⁶ W. Thus the output from every square meter of the Sun's surface is equal to 64 megawatts. Clearly, the spectral radiance of this 1 kW visible transmitter is enormous.

The Columbus Optical SETI Observatory
Copyright (c), 1990